How to make freestyle lines stay the same size?
Yes, it is possible. Here is how:

First change the Line Thickness parameter under Properties tab > Freestyle to Relative (1)



Next go to the Render layers properties, or just click the icon in the Freestyle panel (2). Then go to the thickness tab (3), and then Add a Distance from Camera modifier (4) .
You then have to check the invert box (5) to that the lines decrease in width over the distance. You will see a parameter slider box called Range Max (6) , this value should be the distance of the farthest object away visible in the shot.You can use the Fill Range by selection, or do it manually. In my case the object is about 100BU away. Value Min (7) and Value Max (8)  control the ending width and starting width, respectively. 





Note:


For animations you might have to set keyframes for these values
You can ignore the Base Thickness parameter
The Distance from Object modifier can achieve similar results and may be more suitable for animations.
Lines are drawn based on edges. One long cube is only going to have the same width through, regardless of the modifier.






Final Result: